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An undulatory structure and methods for the fabrication and use thereof. The undulatory structure includes a buckled sheet and one or more work input elements for deforming the buckled sheet in an undulating manner wherein each point in a series of points on a sinuously-shaped profile of the buckled

An undulatory structure and methods for the fabrication and use thereof. The undulatory structure includes a buckled sheet and one or more work input elements for deforming the buckled sheet in an undulating manner wherein each point in a series of points on a sinuously-shaped profile of the buckled sheet travels at least partially along a figure eight-shaped path. The undulatory structure can be adapted for use as a solid-state transducer wherein the buckled sheet provides mechanical advantage without appreciable opposition from elastic restoring forces, thereby achieving improved force, displacement and efficiency characteristics.

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1. A structure comprising: a buckled sheet having a sinuously-shaped profile; andone or more work input elements in communication with the buckled sheet for deforming the buckled sheet in an undulating manner wherein each point in a series of points on the sinuously-shaped profile travels at least p

1. A structure comprising: a buckled sheet having a sinuously-shaped profile; andone or more work input elements in communication with the buckled sheet for deforming the buckled sheet in an undulating manner wherein each point in a series of points on the sinuously-shaped profile travels at least partially along a figure eight-shaped path relative to a common frame of reference. 2. The structure of claim 1, wherein the buckled sheet comprises a material having isotropic mechanical properties. 3. The structure of claim 1, wherein the sinuously-shaped profile is sinusoidally shaped. 4. The structure of claim 1, wherein the sinuously-shaped profile viewed from a section of the buckled sheet has a shape selected from the group consisting of: circumferential, linear, and curved. 5. The structure of claim 1, wherein the sinuously-shaped profile has an amplitude that is characterised in a direction extending normally from the section in a way selected from the group consisting of: substantially constant, monotonic, and sinuously-varying. 6. The structure of claim 1, wherein the buckled sheet is saddle-shaped. 7. A structure, comprising: a buckled sheet having a saddle point and a periphery, wherein a section of the buckled sheet adjacent to the saddle point has a saddle shape; andone or more work input elements connected to the section of the buckled sheet having a saddle shape for acting to rotatably reorientate the saddle shape of the section in relation to the saddle point by deforming the buckled sheet,wherein each point in a series of points on the periphery travels at least partially along a figure eight-shaped path relative to the saddle point. 8. The structure of claim 1 wherein the buckled sheet is deformable in an undulating manner with substantially constant net strain energy, whereby the buckled sheet may be deformed without appreciable opposition from elastic restoring forces. 9. The structure of claim 7 wherein the buckled sheet is deformable in an undulating manner with substantially constant net strain energy, whereby the buckled sheet may be deformed without appreciable opposition from elastic restoring forces. 10. The structure of claim 1, wherein the structure is in the form of one of the following: a transducer; an actuator; a sensor; a generator; a fan; a pump; a loudspeaker; a heat engine; and a propulsion system. 11. The structure of claim 7, wherein the structure is in the form of one of the following: a transducer; an actuator; a sensor; a generator; a fan; a pump; a loudspeaker; a heat engine; and a propulsion system. 12. The structure of claim 1, wherein the structure is a machine for performing work on one or more bodies in communication with the machine, whereby the buckled sheet performs work on the one or more bodies as a result of being deformed in an undulating manner. 13. The structure of claim 7, wherein the structure is a machine for performing work on one or more bodies in communication with the machine, whereby the buckled sheet performs work on the one or more bodies as a result of being deformed in an undulating manner. 14. The structure of claim 13, wherein the buckled sheet is a mechanical transformer configured to provide mechanical advantage between the one or more work input elements and the one or more bodies in communication with the machine. 15. A method for performing work on one or more bodies in communication with a buckled sheet having a sinuously-shaped profile, the method including deforming the buckled sheet wherein each point in a series of points on the sinuously-shaped profile of the buckled sheet travels at least partially along a figure eight-shaped path relative to a common frame of reference whereby the buckled sheet exerts a motion-producing force on the one or more bodies as a result of the deformation. 16. The method of claim 15, wherein the buckled sheet is deformed with substantially constant net strain energy whereby deformation of the buckled sheet is achieved without appreciable opposition from elastic restoring forces. 17. A method of fabricating a structure comprising the steps of: forming a sinuously-shaped profile in a compliant sheet by inducing buckling stresses therein; andproviding at least one work input element in communication with the compliant sheet for causing each point in a series of points on the sinuously-shaped profile to travel a figure eight-shaped path relative to a common frame of reference. 18. The method of claim 17, further comprising the step of joining the compliant sheet to a support. 19. The method of claim 17, wherein the step of forming a sinuously-shaped profile in a compliant sheet comprises the step of (i) externally stressing the compliant sheet or (ii) inducing residual stresses in the compliant sheet. 20. The structure of claim 1 wherein an edge of the buckled sheet opposite the sinuously-shaped profile is connected to a support. 21. The method of claim 17, further comprising the step of elastically balancing the compliant sheet. 22. The method of claim 19, wherein the step of inducing residual stresses in the compliant sheet includes one or more of the forming processes selected from the group of: rolling, peening, planishing, and spinning.